Four dimensional wave propagation simulation in liquid metal with realistic thermal fluctuation

In this paper, we performed a four-dimensional numerical simulation to calculate wave propagation in a thermal fluctuating liquid metal in order to obtain detailed knowledge on a wave propagation in coolant material of a Sodium-cooled Fast reactor (SFR). The wave and the medium are described in three spatial and one temporal dimensions. We made use of a massive data set to describe the fluctuating situation of the medium. This data set was provided by Computational Fluid Dynamics (CFD) with a Large-Eddy Simulation (LES) model, which calculated the temperature field with a higher spatial resolution than Reynolds-Averaged Navier-Stokes turbulence models (RANS). This data set was furthermore obtained from other studies on a numerical and physical experiment called PLAJEST that created mixing jets of liquid metal in order to simulate the status of running SFRs. Because of the limitation of computational resources, previous acoustic studies applied to such a medium could only use the spatial-temporally averaged fluctuating heterogeneity of a medium calculated by RANS turbulence model. This limitation may overlook wave fluctuation because of the difference of the resolution between computational fluid dynamics and acoustic wave length. Our numerical effort allowed us to study the most realistic acoustic wave propagation in liquid metal than in any former studies. A new important result was obtained in this work as we demonstrated that ultrasonic measurements could follow thermal-hydraulic fluctuations in an opaque liquid with high sensitivity. This result was obtained through the definition of descriptors to analyze medium fluctuations along the wave path. We defined a very new measurement index, called hereafter Cumulated Temperature Fluctuation Intensity (CTFI), to correlate the variations in the thermal-hydraulic conditions to the wave variations. We demonstrated a good correlation between the second derivative of this index and the second derivative of several acoustic measurements, then we discussed the easiest measurements to be used in practice in an industrial setup.

Simulation of crack induced nonlinear elasticity using the combined finite-discrete element method

Numerical simulation of nonlinear elastic wave propagation in solids with cracks is indispensable for decoding the complicated mechanisms associated with the nonlinear ultrasonic techniques in Non-Destructive Testing (NDT). Here, we introduce a two-dimensional implementation of the combined finite-discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), to explicitly simulate the crack induced nonlinear elasticity in solids with both horizontal and inclined cracks. In the FDEM model, the solid is discretized into finite elements to capture the wave propagation in the bulk material, and the finite elements along the two sides of the crack also behave as discrete elements to track the normal and tangential interactions between crack surfaces. The simulation results show that for cracked models, nonlinear elasticity is generated only when the excitation amplitude is large enough to trigger the contact between crack surfaces, and the nonlinear behavior is very sensitive to the crack surface contact. The simulations reveal the influence of normal and tangential contact on the nonlinear elasticity generation. Moreover, the results demonstrate the capabilities of FDEM for decoding the causality of nonlinear elasticity in cracked solid and its potential to assist in Non-Destructive Testing (NDT).